1 Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9 Thaddäus Derfflinger’s sunspot observations during 1802-1824: A primary reference to understand the Dalton Minimum Hisashi Hayakawa (1-2)*, Bruno P. Besser (3-4), Tomoya Iju (5), Rainer Arlt (6), Shoma Uneme (7), Shinsuke Imada (7), Philippe-A. Bourdin (4-3), Amand Kraml (8) (1) Graduate School of Letters, Osaka University, 5600043, Toyonaka, Japan (JSPS Research Fellow). (2) UK Solar System Data Centre, Space Physics and Operations Division, RAL Space, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Harwell Oxford, Didcot, Oxfordshire, OX11 0QX, UK (3) Space Research Institute, Austrian Academy of Sciences, Graz, 8042, Austria (4) Institute of Physics, University of Graz, Universitätsplatz 5/II, 8010 Graz, Austria (5) National Astronomical Observatory of Japan, 1818588, Mitaka, Japan. (6) Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany (7) Institute for Space-Earth Environmental Research, Nagoya University, 4648601, Nagoya, Japan (8) Sternwarte, Stift Kremsmünster 4550, Kremsmünster, Austria * [email protected]/[email protected]Abstract As we are heading towards the next solar cycle, presumably with a relatively small amplitude, it is of significant interest to reconstruct and describe the past grand minima on the basis of actual observations of the time. The Dalton Minimum is often considered one of the grand minima captured in the coverage of telescopic observations. Nevertheless, the reconstructions of the sunspot group number vary significantly, and the existing butterfly diagrams have a large data gap during the period. This is partially because most long-term observations have remained unexplored in historical archives. Therefore, to improve our understanding on the Dalton Minimum, we have located two series of Thaddäus Derfflinger's observational records (a summary manuscript and logbooks) as well as his Brander’s 5.5-feet azimuthal-quadrant preserved in the Kremsmünster Observatory. We have revised the existing Derfflinger’s sunspot group number with Waldmeier classification and eliminated all the existing ‘spotless days’ to remove contaminations from solar meridian
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Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
Thaddäus Derfflinger’s sunspot observations during 1802-1824: A primary reference to understand the Dalton Minimum
Hisashi Hayakawa (1-2)*, Bruno P. Besser (3-4), Tomoya Iju (5), Rainer Arlt (6), Shoma Uneme (7),
(3) Space Research Institute, Austrian Academy of Sciences, Graz, 8042, Austria
(4) Institute of Physics, University of Graz, Universitätsplatz 5/II, 8010 Graz, Austria (5) National Astronomical Observatory of Japan, 1818588, Mitaka, Japan.
(6) Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam,
Germany (7) Institute for Space-Earth Environmental Research, Nagoya University, 4648601, Nagoya, Japan
(8) Sternwarte, Stift Kremsmünster 4550, Kremsmünster, Austria
As we are heading towards the next solar cycle, presumably with a relatively small amplitude, it is of
significant interest to reconstruct and describe the past grand minima on the basis of actual
observations of the time. The Dalton Minimum is often considered one of the grand minima captured
in the coverage of telescopic observations. Nevertheless, the reconstructions of the sunspot group
number vary significantly, and the existing butterfly diagrams have a large data gap during the
period. This is partially because most long-term observations have remained unexplored in historical
archives. Therefore, to improve our understanding on the Dalton Minimum, we have located two
series of Thaddäus Derfflinger's observational records (a summary manuscript and logbooks) as well
as his Brander’s 5.5-feet azimuthal-quadrant preserved in the Kremsmünster Observatory. We have
revised the existing Derfflinger’s sunspot group number with Waldmeier classification and
eliminated all the existing ‘spotless days’ to remove contaminations from solar meridian
2
Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
observations. We have reconstructed the butterfly diagram on the basis of his observations and
illustrated sunspot distributions in both solar hemispheres. Our article aims to revise the trend of
Derfflinger’s sunspot group number and to bridge a data gap of the existing butterfly diagrams
around the Dalton Minimum. Our results confirm that the Dalton Minimum is significantly different
from the Maunder Minimum, both in terms of cycle amplitudes and sunspot distributions. Therefore,
the Dalton Minimum is more likely a secular minimum in the long-term solar activity, while further
investigations for the observations at that time are required.
Introduction:
It is important to investigate and reconstruct solar activity of the past as it provides fundamental
input for several fields such as the solar dynamo theory (Charbonneau, 2010; Atlt and Weiss, 2014;
Auguston et al., 2015; Hotta et al., 2016), the solar-terrestrial relationship (Lockwood, 2013;
Hayakawa et al., 2018d, 2019b), space weather (Cliver and Dietrich, 2013; Hayakawa et al., 2017,
2018c, 2019a; Toriumi et al., 2017, 2019), space climate (Hathaway and Wilson, 2004; Owens et al.,
2011; Barnard et al., 2011; Usoskin et al., 2015; Hayakawa et al., 2019c; Pevtsov et al. 2019),
terrestrial climate change (Gray et al., 2010; Lockwood, 2012; Owens et al., 2017), and for
predictions of upcoming solar cycles (Svalgaard et al., 2005; Petrovay, 2010; Iijima et al., 2017;
Upton and Hathaway, 2018). Excluding the solar cycle of approximately 11 years, solar activity has
longer-term variations such as grand minima and grand maxima (Solanki et al., 2004; Solanki and
Krivova, 2004; Usoskin et al., 2007; Clette et al., 2014; Inceoglu et al., 2015; Muscheler et al.,
2016; Usoskin, 2017). Therefore, it is important to investigate the properties of the sunspot number during the grand
minima, on the basis of contemporary observations. Certain predictions suggest the possibility of
another grand minimum in the near future (e.g., Lockwood, 2010; Barnard et al., 2011; Solanki and
Krivova, 2011; Iijima et al., 2017; Upton and Hathaway, 2018). However, we have only two grand
minima within the coverage of direct sunspot observations recorded using telescopes for about 400
years (Hoyt and Schatten, 1998; Clette et al., 2014; Clette and Lefevre, 2016; Vaquero et al., 2016;
Svalgaard and Schatten, 2016), while grand minima and grand maxima are reported in millennial
time scale compiled by multiple cosmogenic isotopes from tree-rings and ice cores (Solanki et al.,
2004; Usoskin et al., 2007; Inceoglu et al., 2015; Usoskin, 2017; Wu et al., 2018). Further, recent revisions of sunspot number based on historical documents require us to re-evaluate
the solar activity for a longer time span (Clette and Lefevre, 2016; Vaquero et al., 2016).
Reconsideration of historical documents also suggests that we should seek to new records (Vaquero
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Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
et al., 2007, 2011; Arlt, 2008, 2009, 2018; Hayakawa et al., 2018a, 2018b; Carrasco et al., 2015,
2016, 2018, 2019b; Denig and McVaugh, 2017), remove apparent continuous spotless days
(Vaquero, 2007; Vaquero et al., 2016), and revise observations based on modern viewpoints
(Vaquero et al., 2016; Svalgaard, 2017; Hayakawa et al., 2018d; Arlt et al., 2013, 2016; Fujiyama et
al., 2019; Karoff et al., 2019; Jørgensen et al., 2019; Pevtsov et al. 2019). Based on these revisions,
a long-term variation of solar activity was evaluated utilising multiple methodologies (Svalgaard and
Schatten, 2016; Usoskin et al., 2016; Clette and Lefevre, 2016; Chatzistergos et al., 2017). The solar
activity during the Maunder Minimum (c.a., 1645–1715) was also reconsidered (Vaquero et al.,
2015; Usoskin et al., 2015, 2017) and the scenario of its onset was notably rewritten (Vaquero et al.,
2011). In this context, it is discussed if the Dalton Minimum (c.a., 1797–1827) should be considered as
one of the grand minima (e.g., Kataoka et al., 2012; McCracken and Beer, 2014) or one of the
secular minima in the long-term solar activity (e.g., Usoskin et al., 2015). So far, this “minimum”
has been studied, including its amplitude and cyclicity (Schüssler et al., 1997; Sokoloff, 2004;
Usoskin et al., 2007; Petrovay, 2010; Usoskin, 2017). After Wolf (1894), the amplitude and cycles
of its primary part have been discussed with contemporary sunspot observations (Hoyt and Schatten,
1992a, 1992b), and in the auroral reports in Europe (Schröder et al., 2004). Recent studies provide
some insights upon the discussions on its onset (Usoskin et al., 2009; Zolotova et al., 2011) with a
revision of the sunspot number (Vaquero et al., 2016; Hayakawa et al., 2018a) and reconstructions
of proxies of cosmogenic isotopes (Karoff et al., 2015; Owens et al., 2015). Further, the recovery of
sunspot observations for this period is ongoing, for example, in the observations recorded by
Jonathan Fisher during 1816–1817 (Denig and McVaugh, 2017) or by Franz Hallaschka during
1814–1816 (Carrasco et al., 2018), to improve the reconstruction of sunspot activity. These studies
have demonstrated that the Dalton Minimum was probably considerably different from the Maunder
Minimum in terms of the duration and the amplitude of solar cycles (e.g., Miyahara et al., 2004;
Usoskin et al., 2007, 2015; Vaquero et al., 2015)
Thaddäus Derfflinger was one of the most active and important long-term observers during the
Dalton Minimum (see Figure 18 of Clette et al., 2014; Figure 2 of Svalgaard and Schatten, 2016;
Figure 1 of Willamo et al., 2017). His sunspot observations were studied by Wolf (1894) long after
Derfflinger’s death and were adopted by Hoyt and Schatten (1998) as they were. However, Wolf
explicitly mentioned that he did not consult the original manuscript but received the information
through a letter from Schwab, one of Derfflinger’s successors as the director of the Kremsmünster
Observatory (Wolf, 1894, pp. 97-98). Further, the classification method of the sunspot groups seems
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Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
slightly different from the early modern times to modern time and hence, is subjected to
reconsideration (e.g., Svalgaard, 2017). Therefore, in this study, we referred to the original
manuscript in the Kremsmünster Observatory, re-examined Derfflinger’s sunspot observations and
to reconstruct the time series of the sunspot group number and measure the sunspot positions
according to the records in the original manuscripts.
2. Observers: Thaddäus Derfflinger and his Assistants
Thaddäus Derfflinger (Figure 1) was born on 19 December 1748 at Mühlwang near Gmunden and
passed away on 18 April 1824 in Kremsmünster (Fellöcker, 1864, pp. 91 – 159). He studied
theology and mathematics at the University of Salzburg and received his priesthood ordination in
Passau. Around 1776, he studied astronomy under Placidus Fixlmillner (1721–1791), the first
astronomer of the Kremsmünster Observatory (N48°03′, E14°08′). When Fixlmillner passed away in
1791, Derfflinger took over the position of director of the observatory and remained there for 33
years until his death (Fellöcker, 1864, p. 92). Kremsmünster Observatory is not situated in Germany
as reported in Hoyt and Schatten (1998) but in Austria under the rule of the Habsburg Empire
(Fellöcker, 1864).
Figure 1: Derfflinger’s portrait in a chalk drawing by Grinzenberger dated 25 April 1797 (courtesy:
Kremsmünster Observatory).
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Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
While Derfflinger experienced the turmoil during the French invasion under Napoleon in 1800 and
1804–1805 (Fellöcker, 1864, p. 96), he continued his sunspot observations even during the second
invasion. He was in regular contact with observatories in Vienna and Prague, including with the
contemporary sunspot observer Franz Hallaschka (Fellöcker, 1864, p. 99–100) whose sunspot
records have been recently recovered (Carrasco et al., 2018). During the last two decades of
Derfflinger life, he suffered from the degradation of his eyesight and lost his left eyesight in spring
1819 (Fellöcker, 1864, p. 92). The loss is partially because of his long-term sunspot observations.
However, he maintained his right eyesight and supervised the sunspot observations until 21 March
1824, one month before his death (Fellöcker, 1864, pp. 93 – 111). Within the monastery, he had two assistants: Benno Waller (1758–1833) and Leander Öttl (1757–
1849), two other monks of the confraternity of Benedictines. He had at least three more assistants
outside of the monastery: Johann Illinger (1724–1800), Simon Lettenmayr (father: 1757–1834), and
Simon Lettenmayr (son: 1787–1868). Johann Illinger had worked in the observatory since the time
of Fixlmillner. Simon Lettenmayr (father) worked not only on the construction and reparation of the
monastery buildings but also as an observational assistant. His son, also named Simon Lettenmayr,
accompanied Derfflinger during his visit to Prague in 1816 and was advised by Hallaschka to
improve and construct observational instruments. He also received basic education in meteorology
and astronomy from the teachers of Kremsmünster School and performed magnetic observations
under the supervision of the observatory directors: Derfflinger, Bonifaz Schwarzenbrunner (1790–
1830), and Marian Koller (1792–1866). Eventually, his eyesight considerably degraded and he
retired (Fellöcker, 1864, pp. 111–112).
3. Observational Records:
Derfflinger’s sunspot records are currently preserved in the directorate archives of the Kremsmünster
Observatory. The sunspot drawings have been recorded both in the meteorological logbooks (v. 2–5)
and the summary manuscript entitled ‘Overview of the sunspots which were observed on the
observatory of Kremsmünster since 26 September 1802 until 1824 inclusive; then as of 26 July 1848
(Uibersicht der Sonnenmackeln welche auf der Sternwarte zu Kremsmünster seit dem 26. September
1802 beobachtet wurden, bis 1824 inclusive; dann vom 26. Juli 1848)’ (see Appendix 1). It is
inferred that there may have been original daily sunspot drawings besides these manuscripts, made
directly at the telescope, as sunspot drawings are cruder in the meteorological logs and more detailed
in the summary manuscript.
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Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
Figure 2: (a) Sunspot observations in 1803 in Derfflinger’s summary manuscript with its footnote (p.
1) and (b) Sunspot drawings dated 25–31 July 1803 involved in meteorological logbooks (v. 2, p.
122). In the right panel, sunspot drawings are shown as tiny circles including dots in which are
placed in a table.
The summary manuscript (Figure 2(a)) explains in its footnote when and why it was compiled:
‘Sunspots, from the diaries of Sun noon observations in Kremsmünster, summarized in February
1825 and following years. The drawings illustrate the sunspots like they have been depicted with the
inverting lens tube of the azimuthal quadrant of Brander ante meridiem at the observation of the
solar altitude’ (Figure 2). This footnote shows that the sunspot observations were a by-product of the
regular solar elevation observations to determine local solar noon since 1802.
Accordingly, this summary collected sunspot drawings around mid-day and was compiled in
February 1825, soon after the death of Derfflinger. It seems to have been planned to collect further
sunspot drawings after 1825, as shown with the unfilled margin for 1825 without sunspot drawings
(summary manuscript, p. 7). Further, a sunspot drawing on 26 July 1848 with at least 9 sunspot
groups was included by an anonymous observer, possibly associated with Augustin Reslhuber,
director of Kremsmünster Observatory at the time. On this date, both Schwabe and Shea reported 6
sunspot groups (Vaquero et al., 2016).
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Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
4. Instruments and Telescopes:
Since 1802, the Kremsmünster Observatory (Figure 3(a)) monitored the position of the Sun on a
regular basis to time the true local noon with the aid of a transportable quadrant. By measuring
various timings of given elevations of the Sun in the morning and in the afternoon, the solar
culmination can be computed and the time of true local noon determined. During these
measurements, sunspots have been recognised quite frequently and small sunspot sketches have been
recorded into the meteorological logbooks (Figure 2(b)).
Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
compatible with its modern shape and that the differences to modern graphs are not significant and
attributable to the limited accuracy of the observations.
Error margins of the heliographic positions were obtained in the following way. As the primary
unknown quantity in the analysis is the position angle of the solar disk, we assumed a general
uncertainty of ±10 degrees in the position angle. We then employed this uncertainty to the
conversion of the spot locations into heliographic positions and obtained individual uncertainties for
the heliographic longitudes and latitudes. In the case of rotational matching, the results are
probability density distributions of all unknown quantities with 68% confidence intervals. We did
not measure nearly circular arcs around sunspots that appear to denote penumbrae of evolving spots.
However, non-circular arcs rather look like chains of smaller spots and were measured.
Figure 8: A reconstructed butterfly diagram for sunspot positions in Derfflinger’s manuscript. This
diagram is divided into blocks of 27-day duration at 3 degrees latitude range. The numbers of spots
falling into these bins are counted. The darkness of the blue represents the number of spots counted
in a bin. The spots with light blue represent 1 and 2 spots, those with medium blue represent 3–5
spots, those with dark blue represent 6–8 spots, and those with violet represent 9–12 spots.
10. Conclusions and Outlooks
In this article, we have examined Derfflinger’s sunspot observations on the basis of his original
records. Derfflinger’s observations are currently preserved in the directorate archives of the
Kremsmünster Observatory as a summary manuscript and meteorological logbooks (v. 2–5).
Derfflinger conducted his sunspot observations from 1802 to 1824 with aids of his assistants, as by-
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Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
products of solar elevation observations. Derfflinger used Brander’s 5.5-feet azimuthal-quadrant for
the observations of sunspots and of the solar elevation. Examining his original observational records, we have discovered that the existing ‘spotless days’
were contaminations from solar elevation observations without sunspot drawings. Accordingly, these
‘spotless days’ were eliminated, as they do not necessarily mean the absence of sunspots. In contrast,
we found evidence that there were sunspots at least in some of those removed data. We have also
against the register in the existing dataset (Hoyt and Schatten, 1998; Vaquero et al., 2016). We then
applied the Waldmeier classification to revise Derfflinger’s group sunspot number. The revised
Derfflinger’s trend shows that the amplitude of Cycle 5 is slightly higher than that of Cycle 6. The
revised trend seems rather consistent with the Sunspot Number (version 2) in Cycle 5, whereas his
revised trend in Cycle 6 is more consistent with the group sunspot number series. We have reconstructed the butterfly diagram on the basis of Derfflinger’s sunspot observations and
have filled the existing data gap (see Muñoz-Jaramillo and Vaquero, 2019). The reconstructed
butterfly diagram demonstrates no significant asymmetry of sunspot distributions like that of the
Maunder Minimum (Ribes and Nesme-Ribes, 1993). We observed considerable sunspots near the
solar equator, probably due to the limited quality of Derfflinger’s sunspot observations.
Our revision shows that Derfflinger’s sunspot cycles during the Dalton minimum have a slightly
higher amplitude of the solar activity than previously considered. The data gap of the butterfly
diagram in this period has been filled and does not show extremely asymmetric sunspot distributions
like those of the Maunder Minimum. Our reconstruction shows that the Dalton minimum was
significantly different from the Maunder minimum, either in terms of cycle amplitude (c.f., Usoskin
et al., 2015), its duration (c.f., Miyahara et al., 2004; Vaquero et al., 2015), or its more symmetric
butterfly diagram (c.f., Ribes and Nesme-Ribes, 1993).
Primarily, the reconstructed cycles during the Dalton Minimum were approximately 11 years (≈ 12
years), while the period during the Maunder minimum was probably either considerably shorter
(Vaquero et al., 2015) or longer (Miyahara et al., 2004) than 11 years. A peculiarity of the early
Dalton minimum was a ‘hiccup’ in the cycle period. This may have been either a very long cycle of
approximately 15 years duration (Hathaway, 2015) or a short cycle followed by a very weak one of,
respectively, a little less than 9 years and more than 7 years (Usoskin et al., 2009). That period falls
before Derfflinger’s observations.
Our study hints to an understanding of the Dalton minimum as not towards a grand minimum
characterized with extremely weak or even collapsed solar dynamo cycles, but more towards a
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Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
secular minimum in the long-term solar activity slightly longer cycles with low activity. This notion
is more consistent with a solar dynamo that continued to produce a reasonable number of sunspots
during the Dalton minimum. Potential deviations from the average cycle length are probably
determined by quantities which are difficult to access in historical observations, such as the
meridional circulation, stochastic variations in the convective patterns, or the internal rise time of
magnetic flux to the solar surface (e.g., Charbonneau, 2013, Chapter 4; Fournier et al., 2018).
Nevertheless, it has been determined that Derfflinger did not record spotless days during his
observations and the cycle amplitudes during the Dalton Minimum may be revised slightly
downward. We are required to carefully revise the data of other contemporary sunspot observers
during the Dalton minimum, revise the actual group number, and define the actual spotless days.
Additionally, spot areas are to be studied further owing to their seemingly exaggerated size as
observed in other historical observations using aerial imaging method (see e.g., Fujiyama et al.,
2019; Karachik et al., 2019). Further research on the Dalton minimum will improve our knowledge
of solar activity during the solar minima or the suppressed solar cycles.
Acknowledgement
We thank Kremsmünster Observatory for permitting access to Derfflinger’s manuscripts and for the
reproduction of some observational records as well as preserving these records. HH thanks F. Clette
and S. Toriumi for their helpful comments. This research has been conducted with aids of
KAKENHI Grant Number 15H05812 (PI: K. Kusano), JP15H05816 (PI: S. Yoden), and JP17J06954
(PI: H. Hayakawa), as well as the Austrian Science Foundation (FWF) project P 31088 (PI: U.
Fölsche) and the Deutsche Forschungsgemeinschaft grant number AR355/12-1 (PI: R. Arlt). This
work has been partly merited from participation to the International Space Science Institute (ISSI,
Bern, Switzerland) via the International Team 417 “Recalibration of the Sunspot Number Series”.
Appendix 1: Historical Sources
Summary Manuscript: Uibersicht der Sonnenmackeln, welche auf der Sternwarte zu Kremsmünster
Seit dem 26. September 1802 beobachtet wurden. bis 1824 inclusive; dann vom 26. Juli 1848,
MS, Direktions-Archiv der Sternwarte Kremsmünster
Logbook (v.2): Meteorologische Beobachtungen zu Kremsmünster 1801-1807, II. Bd. MS,
Direktions-Archiv der Sternwarte Kremsmünster
Logbook (v.3): Meteorologische Beobachtungen zu Kremsmünster 1808-1813, III. Bd. MS,
Direktions-Archiv der Sternwarte Kremsmünster
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Hayakawa et al. (2020) Thaddäus Derfflinger’s sunspot observations during 1802-1824, The Astrophysical Journal, doi: 10.3847/1538-4357/ab65c9
Logbook (v.4): Meteorologische Beobachtungen zu Kremsmünster 1814-19, IV. Bd. MS,
Direktions-Archiv der Sternwarte Kremsmünster
Logbook (v.5): Meteorologische Beobachtungen zu Kremsmünster 1820-25, V. Bd. MS, Direktions-
Archiv der Sternwarte Kremsmünster
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